A note on small periodic solutions of discrete nonlinear Klein-Gordon equations

Abstract

In this note, we consider discrete nonlinear Klein-Gordon equations with potential. By the pioneering work of Sigal, it is known that for the "continuous" nonlinear Klein-Gordon equation, no small time periodic solution exists generically. However, for the discrete nonlinear Klein-Gordon equations, we show that there exist small time periodic solutions.

10 pages, to appear in RIMS Kokyuroku Bessatsu

References in corpus (1)

• Existence and asymptotic stability of quasi-periodic solution of discrete NLS with potential in $\mathbb{Z}$